Math Calendar

 Categories: Choose a category... View all categories _______________________ Biomath Seminar Colloquium Computational Analysis Seminar Departmental Student Awards Faculty Meeting Graph Theory and Combinatorics Seminar Informal von Neumann Algebras Seminar Noncommutative Geometry and Operator Algebras Seminar Partial Differential Equations Seminar Subfactor Seminar Symplectic and Differential Geometry Seminar Topology and Group Theory Seminar Undergraduate Seminar Universal Algebra and Logic Seminar Vandy Math Club RSS

» Seminar Pages

October 21, 2013 3:00 pm (Monday)

Unique Cartan Subalgebras and Solidity Results for II_1 factors

Chenxu Wen, Vanderbilt University
Location: Stevenson 1404

The recent development in the rigidity results in the study of II_1 factors from the group-measure-space construction has lead to many new insights to the structure of certain factors. Of particular importance in the theory is the unique Cartan subalgebra (or group-measure-space Cartan), up to unitary conjugacy, for some II_1 factors. In the talk we will discuss the work in this direction started by Ozawa and Popa and followed by many others. As the consequence of the techniques involved, we will also talk about some solidity results for some group von Neumann algebras.

October 21, 2013 3:10 pm (Monday)

Circumference and Pathwidth of Highly Connected Graphs

Emily Marshall, Vanderbilt University
Location: Stevenson 1432

Birmele proved that every graph with circumference t has treewidth at most t-1. Under the additional assumption of 2-connectivity, results of Nesetril and Ossona de Mendez show that such graphs have bounded pathwidth, which is a qualitatively stronger conclusion. We make a factor-2 improvement to their bound. Birmele's theorem was extended by Birmele, Bondy and Reed who showed that every graph without k disjoint cycles of length at least t has bounded treewidth (as a function of k and t). Our main result states that, under the additional assumption of (k + 1) connectivity, such graphs have bounded pathwidth. In fact, they have pathwidth O(t^3 + tk^2). Moreover, examples show that (k + 1)-connectivity is required for bounded pathwidth to hold. These results suggest the following general question: for which values of k and graphs H does every k-connected H-minor-free graph have bounded pathwidth? We discuss this question and provide a few observations. This is joint work with David Wood at Monash University.

October 22, 2013 6:00 pm (Tuesday)

Brian Simanek, Vanderbilt University
Location: Stevenson 1206

Our mathematics education parallels the history of mathematics in that it all began with counting.  At a very young age, we understood the idea of quantity and - more importantly - how to compare quantities.  Then, somewhere along the way we vaguely became aware of this mysterious idea called infinity that somehow answered the question we all posed to our first grade teachers: "What is the largest number?"  The main point of this talk will be to demonstrate that infinity does not really answer this question because there are different sizes of infinity!  As strange as this may seem, we will try to understand how this can be the case and mention some different ways that mathematicians describe the size of a set when counting is not sufficient.

October 23, 2013 3:30 pm (Wednesday)

Location: Stevenson 1425

October 23, 2013 4:10 pm (Wednesday)

Groups With a Tree-Graded Asymptotic Cone

Rémi Coulon, Vanderbilt University
Location: Stevenson 1310

Given a finitely generated group G, its asymptotic cones is a class of objects that capture the large scale properties of the group. Roughly speaking they are obtained by looking at G from infinitely far away. The asymptotic cones of a hyperbolic group are trees. Conversely if G is a finitely presented group such that some asymptotic cone of G is a tree, then G is hyperbolic. The goal of this talk is to present a generalization of this statement for the class of relatively hyperbolic groups. This is a joint work with M. Hull and C. Kent.

October 24, 2013 4:10 pm (Thursday)

Alice Guionnet, MIT
Location: Stevenson 5211

Maps are connected graphs which are properly embedded into a surface, their genus is the minimal genus of such a surface. Matrix integrals have been shown to be related with the enumeration of maps since the seventies, after the work of 't Hooft and Br\'ezin-Itzykson-Parisi and Zuber. This is the so-called topological expansion. Such an expansion has been used in many fields of physics and mathematics. In this talk, we shall describe this correspondence, discuss some applications and some generalizations. Tea at 3:30 pm in SC 1425.

October 25, 2013 2:10 pm (Friday)

Ultraproducts, QWEP von Neumann Algebras, and the Effros-MarĂ©chal Topology

Uffe Haagerup, University of Copenhagen
Location: Stevenson 1310

The talk is based on a joint work with Hiroshi Ando and Carl Winslöw (arXiv:1306.0460). Based on analysis on the Ocneanu/Groh-Raynaud ultraproducts and the Effros-Maréchal topology on the space vN(H) of von Neumann algebras acting on a separable Hilbert space H, we show that for a von Neumann algebra M in vN(H), the following conditions are equivalent: (1) M has the Kirhcberg's quotient weak expectation property (QWEP). (2) M is in the closure of the set of injective factors on H with respect to the Effros-Maréchal topology. (3) M admits an embedding i into the Ocneanu ultrapower N^omega of the injective III_1 factor N with a normal faithful conditional expectation from N^omega to M. (4) For every epsilon > 0, natural number n, and x_1,...,x_n in natural cone P_M^{natural} in the standard form for M, there is a natural number k and a_1,...,a_n in M_k(C)_+, such that | < x_i, x_j > - tr_k(a_ia_j) | is less than epsilon for i,j = 1,...,n, where tr_k is the tracial state on M_k(C).

October 26, 2013 9:00 am (Saturday)

DARPA & Shanks Workshop: "Quantum Symmetries"

Location: Stevenson 1432

In this two-day workshop, Oct. 26-27, several participants will report on progress on DARPA funded research projects. Other talks will cover areas that could be broadly described as quantum symmetries. For more information, see the conference website: http://www.math.vanderbilt.edu/~bisch/quantum_symmetries.html

October 27, 2013 9:00 am (Sunday)

DARPA & Shanks Workshop: "Quantum Symmetries"

Location: Stevenson 1432

In this two-day workshop, Oct. 26-27, several participants will report on progress on DARPA funded research projects. Other talks will cover areas that could be broadly described as quantum symmetries. For more information, see the conference website: http://www.math.vanderbilt.edu/~bisch/quantum_symmetries.html